Relativistic Magnetohydrodynamics

Abstract
The relativistic equations of motion for a conducting fluid in a magnetic field are formulated. A relativistically correct equation for the production of entropy due to Joule heating is derived from the conservation laws for mass, momentum, and energy. It is shown that both the energy density of the magnetic field and the magnetic pressure contribute to the inertia of a perfectly conducting fluid. The general dispersion relation for small-amplitude oscillations is found.